When next you board a British Airways plane, think twice before abusing your call button: there's a good chance ­whoever answers is being paid nothing for the ­privilege of fetching that extra pillow.

All of BA's 40,000 staff have been made what could be described as a missable offer: the chance to work for free for up to a month. Though it sounds like a bad joke, the reasons behind the request are deadly serious. The company recently reported pre-tax losses of £401m.

The wheeze is outlined in the latest ­edition of BA's in-house magazine under the headline Action Time: "Colleagues are being urged to help the airline's ­cash-saving drive by signing up for unpaid leave or unpaid work. From tomorrow, people will be able to opt for blocks of unpaid leave or unpaid work, with ­salary deductions spread over three to six months, wherever possible."

The article in BA News conceded unpaid work would be tantamount to accepting a cut in pay, which Willie Walsh, the chief executive, is keen to negotiate across the airline in what he calls the "fight for survival." "The new unpaid work option means people can contribute to the cash-saving effort by coming to work while effectively volunteering for a small cut in base pay," said Walsh, adding that he was looking for "every single part of the company" to get involved.

Walsh, along with Keith Williams, the chief financial officer, has promised to work for nothing in July. But the idea has gone down badly with unions. They point out that Walsh, on a salary of £735,000, can afford a month with no pay, while his subordinates will seriously struggle. The average salary for BA's cabin staff is £29,900, according to the Civil Aviation Authority.

BA's biggest union, Unite, gave the request short shrift. "Willie Walsh can afford to work for nothing, our members can't," said a Unite spokesman.

The only thing more surprising than the idea of a FTSE 100 company daring to ask its employees to work for nothing is the fact that many of its workers have already volunteered to do so. Hundreds of staff have already expressed in interest in working for free, a BA spokeswoman insisted yesterday.

There are only two reasons this could be the case, according to David Guest, professor in organisational psychology at King's College London.

"Either they have high levels of commitment to the firm," he said, "or they have high levels of insecurity."

As Walsh has refused to rule out compulsory redundancies at the airline, you don't need paying to work out which of the above is the most likely motivator.